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main_tyre_data_analysis_orig.asv
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%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% FY %
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% INITIALISE: ------------------------------------------------------------
close all;
clear all;
clc;
% Set LaTeX as default interpreter for axis labels, ticks and legends
set(0,'defaulttextinterpreter','latex')
set(groot, 'defaultAxesTickLabelInterpreter','latex');
set(groot, 'defaultLegendInterpreter','latex');
set(0,'DefaultFigureWindowStyle','docked');
set(0,'defaultAxesFontSize', 16)
set(0,'DefaultLegendFontSize',16)
addpath('tyre_lib/')
to_rad = pi/180;
to_deg = 180/pi;
%% SELECT TYRE DATA -------------------------------------------------------
%dataset path
data_set_path = 'TTC_dataset/';
% dataset selection and loading
% Hoostier:----------------------------------------------------------------
data_set = 'Hoosier_B1464run23'; % pure lateral forces
%data_set = 'Hoosier_B1464run30'; % braking/traction (pure log. force) + combined
fprintf('Loading dataset ...')
switch data_set
case 'Hoosier_B1464run23'
load ([data_set_path, 'Hoosier_B1464run23.mat']); % pure lateral
cut_start = 27760;
cut_end = 54500;
case 'Hoosier_B1464run30'
load ([data_set_path, 'Hoosier_B1464run30.mat']); % pure longitudinal
cut_start = 19028;
cut_end = 37643;
otherwise
error('Not found dataset: `%s`\n', data_set) ;
end
diameter = 18*2.56; % Converting inches to cm
Fz0 = 220; % [N] nominal load is given
R0 = diameter/2/100; % [m] get from nominal load R0 (m)
% select dataset portion
smpl_range = cut_start:cut_end;
fprintf('completed!\n')
%% PLOT RAW DATA ----------------------------------------------------------
figure
tiledlayout(6,1)
ax_list(1) = nexttile; y_range = [min(min(-FZ),0) round(max(-FZ)*1.1)];
plot(-FZ)
hold on
plot([cut_start cut_start],y_range,'--r')
plot([cut_end cut_end],y_range,'--r')
title('Vertical force')
xlabel('Samples [-]')
ylabel('[N]')
ax_list(2) = nexttile; y_range = [min(min(IA),0) round(max(IA)*1.1)];
plot(IA)
hold on
plot([cut_start cut_start],y_range,'--r')
plot([cut_end cut_end],y_range,'--r')
title('Camber angle')
xlabel('Samples [-]')
ylabel('[deg]')
ax_list(3) = nexttile; y_range = [min(min(SA),0) round(max(SA)*1.1)];
plot(SA)
hold on
plot([cut_start cut_start],y_range,'--r')
plot([cut_end cut_end],y_range,'--r')
title('Side slip')
xlabel('Samples [-]')
ylabel('[deg]')
ax_list(4) = nexttile; y_range = [min(min(SL),0) round(max(SL)*1.1)];
plot(SL)
hold on
plot([cut_start cut_start],y_range,'--r')
plot([cut_end cut_end],y_range,'--r')
title('Longitudinal slip')
xlabel('Samples [-]')
ylabel('[-]')
ax_list(5) = nexttile; y_range = [min(min(P),0) round(max(P)*1.1)];
plot(P)
hold on
plot([cut_start cut_start],y_range,'--r')
plot([cut_end cut_end],y_range,'--r')
title('Tyre pressure')
xlabel('Samples [-]')
ylabel('[psi]')
ax_list(6) = nexttile; y_range = [min(min(TSTC),0) round(max(TSTC)*1.1)];
plot(TSTC,'DisplayName','Center')
hold on
plot(TSTI,'DisplayName','Internal')
plot(TSTO,'DisplayName','Outboard')
hold on
plot([cut_start cut_start],y_range,'--r')
plot([cut_end cut_end],y_range,'--r')
title('Tyre temperatures')
xlabel('Samples [-]')
ylabel('[degC]')
linkaxes(ax_list,'x')
%figure()
%plot(SA,FY)
%% SELECT SPECIFIC DATA ---------------------------------------------------
% Cut crappy data and select only 80 psi data
vec_samples = 1:1:length(smpl_range);
tyre_data = table(); % create empty table
% store raw data in table
tyre_data.SL = SL(smpl_range); % Longitudinal slip
tyre_data.SA = SA(smpl_range)*to_rad; % Side slip
tyre_data.FZ = -FZ(smpl_range); % 0.453592 lb/kg % Vertical force
tyre_data.FX = FX(smpl_range); % Longitudinal force
tyre_data.FY = -FY(smpl_range); % Lateral force
tyre_data.MZ = MZ(smpl_range); % Self aligning moment
tyre_data.IA = IA(smpl_range)*to_rad; % Camber angle
% Extract points at constant camber inclination angle
GAMMA_tol = 0.05*to_rad;
idx.GAMMA_0 = 0.0*to_rad-GAMMA_tol < tyre_data.IA & tyre_data.IA < 0.0*to_rad+GAMMA_tol;
idx.GAMMA_1 = 1.0*to_rad-GAMMA_tol < tyre_data.IA & tyre_data.IA < 1.0*to_rad+GAMMA_tol;
idx.GAMMA_2 = 2.0*to_rad-GAMMA_tol < tyre_data.IA & tyre_data.IA < 2.0*to_rad+GAMMA_tol;
idx.GAMMA_3 = 3.0*to_rad-GAMMA_tol < tyre_data.IA & tyre_data.IA < 3.0*to_rad+GAMMA_tol;
idx.GAMMA_4 = 4.0*to_rad-GAMMA_tol < tyre_data.IA & tyre_data.IA < 4.0*to_rad+GAMMA_tol;
idx.GAMMA_5 = 5.0*to_rad-GAMMA_tol < tyre_data.IA & tyre_data.IA < 5.0*to_rad+GAMMA_tol;
GAMMA_0 = tyre_data( idx.GAMMA_0, : );
GAMMA_1 = tyre_data( idx.GAMMA_1, : );
GAMMA_2 = tyre_data( idx.GAMMA_2, : );
GAMMA_3 = tyre_data( idx.GAMMA_3, : );
GAMMA_4 = tyre_data( idx.GAMMA_4, : );
GAMMA_5 = tyre_data( idx.GAMMA_5, : );
% Extract points at constant vertical load
% 200, 150, 50, 250, 100
FZ_tol = 100;
idx.FZ_220 = 220-FZ_tol < tyre_data.FZ & tyre_data.FZ < 220+FZ_tol;
idx.FZ_440 = 440-FZ_tol < tyre_data.FZ & tyre_data.FZ < 440+FZ_tol;
idx.FZ_700 = 700-FZ_tol < tyre_data.FZ & tyre_data.FZ < 700+FZ_tol;
idx.FZ_900 = 900-FZ_tol < tyre_data.FZ & tyre_data.FZ < 900+FZ_tol;
idx.FZ_1120 = 1120-FZ_tol < tyre_data.FZ & tyre_data.FZ < 1120+FZ_tol;
FZ_220 = tyre_data( idx.FZ_220, : );
FZ_440 = tyre_data( idx.FZ_440, : );
FZ_700 = tyre_data( idx.FZ_700, : );
FZ_900 = tyre_data( idx.FZ_900, : );
FZ_1120 = tyre_data( idx.FZ_1120, : );
% The slip angle is varied continuously between -4 and +12° and then
% between -12° and +4° for the pure slip case
% The slip angle is varied step wise for longitudinal slip tests
% 0° , - 3° , -6 °
SA_tol = 0.5*to_rad;
idx.SA_0 = 0-SA_tol < tyre_data.SA & tyre_data.SA < 0+SA_tol;
idx.SA_3neg = -(3*to_rad+SA_tol) < tyre_data.SA & tyre_data.SA < -3*to_rad+SA_tol;
idx.SA_6neg = -(6*to_rad+SA_tol) < tyre_data.SA & tyre_data.SA < -6*to_rad+SA_tol;
SA_0 = tyre_data( idx.SA_0, : );
SA_3neg = tyre_data( idx.SA_3neg, : );
SA_6neg = tyre_data( idx.SA_6neg, : );
figure()
tiledlayout(3,1)
ax_list(1) = nexttile;
plot(tyre_data.IA*to_deg)
hold on
plot(vec_samples(idx.GAMMA_0),GAMMA_0.IA*to_deg,'.');
plot(vec_samples(idx.GAMMA_1),GAMMA_1.IA*to_deg,'.');
plot(vec_samples(idx.GAMMA_2),GAMMA_2.IA*to_deg,'.');
plot(vec_samples(idx.GAMMA_3),GAMMA_3.IA*to_deg,'.');
plot(vec_samples(idx.GAMMA_4),GAMMA_4.IA*to_deg,'.');
plot(vec_samples(idx.GAMMA_5),GAMMA_5.IA*to_deg,'.');
title('Camber angle')
xlabel('Samples [-]')
ylabel('[deg]')
ax_list(2) = nexttile;
plot(tyre_data.FZ)
hold on
plot(vec_samples(idx.FZ_220),FZ_220.FZ,'.');
plot(vec_samples(idx.FZ_440),FZ_440.FZ,'.');
plot(vec_samples(idx.FZ_700),FZ_700.FZ,'.');
plot(vec_samples(idx.FZ_900),FZ_900.FZ,'.');
plot(vec_samples(idx.FZ_1120),FZ_1120.FZ,'.');
title('Vertical force')
xlabel('Samples [-]')
ylabel('[N]')
ax_list(3) = nexttile;
plot(tyre_data.SA*to_deg)
hold on
plot(vec_samples(idx.SA_0), SA_0.SA*to_deg,'.');
plot(vec_samples(idx.SA_3neg),SA_3neg.SA*to_deg,'.');
plot(vec_samples(idx.SA_6neg),SA_6neg.SA*to_deg,'.');
title('Slide slip')
xlabel('Samples [-]')
ylabel('[rad]')
%% PURE LATERAL SLIP FITTING with Fz=Fz_nom= 220N and camber=0 kappa = 0 VX= 10 ----------> DONE
% Initialise:
tyre_coeffs = initialise_tyre_data(R0, Fz0);
[TData0, ~] = intersect_table_data( GAMMA_0, FZ_220 );
FZ0 = mean(TData0.FZ);
zeros_vec = zeros(size(TData0.SA));
ones_vec = ones(size(TData0.SA));
ALPHA_vec = TData0.SA;
FY_vec = TData0.FY;
% Guess values for parameters to be optimised
% [pCy1, pDy1, pEy1, pHy1, pKy1, pKy2, pVy1]
P0 = [ 1, 2, -1, 1, 1, 1, 0];
% NOTE: many local minima => limits on parameters are fundamental
% Limits for parameters to be optimised
% 1< pCx1 < 2
% 0< pEx1 < 1
% [pCy1, pDy1, pEy1, pHy1, pKy1, pKy2, pVy1]
lb = [];
ub = [];
% LSM_pure_Fy returns the residual, so minimize the residual varying Y. It
% is an unconstrained minimization problem
[P_fz_nom,~,~] = fmincon(@(P)resid_pure_Fy(P,FY_vec, ALPHA_vec,0,FZ0, tyre_coeffs),...
P0,[],[],[],[],lb,ub);
% Update tyre data with new optimal values
tyre_coeffs.pCy1 = P_fz_nom(1) ; % 1
tyre_coeffs.pDy1 = P_fz_nom(2) ;
tyre_coeffs.pEy1 = P_fz_nom(3) ;
tyre_coeffs.pHy1 = P_fz_nom(4) ;
tyre_coeffs.pKy1 = P_fz_nom(5) ;
tyre_coeffs.pKy2 = P_fz_nom(6) ;
tyre_coeffs.pVy1 = P_fz_nom(7) ;
SA_vec = min(ALPHA_vec):0.001:max(ALPHA_vec);
FY0_fz_nom_vec = MF96_FY0_vec(zeros(size(SA_vec)), SA_vec, zeros(size(SA_vec)), ...
FZ0.*ones(size(SA_vec)),tyre_coeffs);
figure('Name','Fy0(Fz0)')
plot(TData0.SA,TData0.FY,'.')
hold on
%plot(TDataSub.KAPPA,FX0_fz_nom_vec,'-')
plot(SA_vec,FY0_fz_nom_vec,'-','LineWidth',2)
xlabel('$\alpha$ [deg]')
ylabel('$F_{y0}$ [N]')
legend('Raw data','Fitting',Location='best')
title('Fit pure lateral force $F_{y0}$')
%% VARIABLE LOAD LATERAL FY ---------------------------------------------------------------> DONE
% extract data with variable load
TDataDFz = GAMMA_0;
% Initialise:
zeros_vec = zeros(size(TDataDFz.SA));
ones_vec = ones(size(TDataDFz.SA));
KAPPA_vec = TDataDFz.SL;
ALPHA_vec = TDataDFz.SA;
FY_vec = TDataDFz.FY;
FZ_vec = TDataDFz.FZ;
% Guess for parameters to be optimised:
% [ pDy2, pEy2, pHy2, pVy2]
P0_pure_varFZ = [ -0.274390567365254, -0.278086233494965, -0.00117998967899828, -0.040168008694034];
lb_pure_varFZ = [];
ub_pure_varFZ = [];
% Optimisation:
[P_dfz,~,~] = fmincon(@(P)resid_pure_Fy_varFz(P,FY_vec, ALPHA_vec,0,FZ_vec, tyre_coeffs),...
P0_pure_varFZ,[],[],[],[],lb_pure_varFZ,ub_pure_varFZ);
% Update tyre data with new optimal values
tyre_coeffs.pDy2 = P_dfz(1) ;
tyre_coeffs.pEy2 = P_dfz(2) ;
tyre_coeffs.pHy2 = P_dfz(3) ;
tyre_coeffs.pVy2 = P_dfz(4) ;
SA_vec = min(ALPHA_vec):1e-4:max(ALPHA_vec);
tmp_zeros = zeros(size(SA_vec));
tmp_ones = ones(size(SA_vec));
% Visulisation--- use mean(Fz to avoid oscilltion)
FY0_fz_var_vec1 = MF96_FY0_vec(tmp_zeros, SA_vec, tmp_zeros, mean(FZ_220.FZ)*tmp_ones,tyre_coeffs);
FY0_fz_var_vec2 = MF96_FY0_vec(tmp_zeros, SA_vec, tmp_zeros, mean(FZ_440.FZ)*tmp_ones,tyre_coeffs);
FY0_fz_var_vec3 = MF96_FY0_vec(tmp_zeros, SA_vec, tmp_zeros, mean(FZ_700.FZ)*tmp_ones,tyre_coeffs);
FY0_fz_var_vec4 = MF96_FY0_vec(tmp_zeros, SA_vec, tmp_zeros, mean(FZ_900.FZ)*tmp_ones,tyre_coeffs);
FY0_fz_var_vec5 = MF96_FY0_vec(tmp_zeros, SA_vec, tmp_zeros, mean(FZ_1120.FZ)*tmp_ones,tyre_coeffs);
figure('Name','Fy0(Fz0)')
plot(TDataDFz.SA,TDataDFz.FY,'.')
hold on
plot(SA_vec,FY0_fz_var_vec1,'-','LineWidth',2,Color = [0.8500 0.3250 0.0980])
plot(SA_vec,FY0_fz_var_vec2,'-','LineWidth',2,Color = [0.9290 0.6940 0.1250])
plot(SA_vec,FY0_fz_var_vec3,'-','LineWidth',2,Color = [0.4940 0.1840 0.5560])
plot(SA_vec,FY0_fz_var_vec4,'-','LineWidth',2,Color = [0.4660 0.6740 0.1880])
plot(SA_vec,FY0_fz_var_vec5,'-','LineWidth',2,Color = [0.6350 0.0780 0.1840])
legend('','Fit $F_z = 220$ N', 'Fit $F_z = 440$ N', 'Fit $F_z = 700$ N', 'Fit $F_z = 900$ N', 'Fit $F_z = 1120$ N' , Location='best');
xlabel('$\alpha$ [-]');
ylabel('$F_{y0}$ [N]');
title('Pure lateral slip at different vertical loads')
res_FY0_dfz_vec = resid_pure_Fy_varFz(P_dfz,FY_vec,SA_vec,0 , FZ_vec,tyre_coeffs);
%% CORNERING STIFFNESS --------------------------------------------------------------------> DONE
[alpha__y, By, Cy, Dy, Ey, SVy, ~, ~, ~] =MF96_FY0_coeffs(0, 0, 0, mean(FZ_220.FZ), tyre_coeffs);
Calfa_vec1_0 = magic_formula_stiffness(alpha__y, By, Cy, Dy, Ey, SVy);
[alpha__y, By, Cy, Dy, Ey, SVy, ~, ~, ~] =MF96_FY0_coeffs(0, 0, 0, mean(FZ_440.FZ), tyre_coeffs);
Calfa_vec2_0 = magic_formula_stiffness(alpha__y, By, Cy, Dy, Ey, SVy);
[alpha__y, By, Cy, Dy, Ey, SVy, ~, ~, ~] =MF96_FY0_coeffs(0, 0, 0, mean(FZ_700.FZ), tyre_coeffs);
Calfa_vec3_0 = magic_formula_stiffness(alpha__y, By, Cy, Dy, Ey, SVy);
[alpha__y, By, Cy, Dy, Ey, SVy, ~, ~, ~] =MF96_FY0_coeffs(0, 0, 0, mean(FZ_900.FZ), tyre_coeffs);
Calfa_vec4_0 = magic_formula_stiffness(alpha__y, By, Cy, Dy, Ey, SVy);
[alpha__y, By, Cy, Dy, Ey, SVy, ~, ~, ~] =MF96_FY0_coeffs(0, 0, 0, mean(FZ_1120.FZ), tyre_coeffs);
Calfa_vec5_0 = magic_formula_stiffness(alpha__y, By, Cy, Dy, Ey, SVy);
Calfa_vec1 = MF96_CorneringStiffnessFY(tmp_zeros, SA_vec, tmp_zeros, mean(FZ_220.FZ)*tmp_ones,tyre_coeffs);
Calfa_vec2 = MF96_CorneringStiffnessFY(tmp_zeros, SA_vec, tmp_zeros, mean(FZ_440.FZ)*tmp_ones,tyre_coeffs);
Calfa_vec3 = MF96_CorneringStiffnessFY(tmp_zeros, SA_vec, tmp_zeros, mean(FZ_700.FZ)*tmp_ones,tyre_coeffs);
Calfa_vec4 = MF96_CorneringStiffnessFY(tmp_zeros, SA_vec, tmp_zeros, mean(FZ_900.FZ)*tmp_ones,tyre_coeffs);
Calfa_vec5 = MF96_CorneringStiffnessFY(tmp_zeros, SA_vec, tmp_zeros, mean(FZ_1120.FZ)*tmp_ones,tyre_coeffs);
figure('Name','C_alpha')
subplot(2,1,1)
hold on
%plot(TDataSub.KAPPA,FX0_fz_nom_vec,'-')
plot(mean(FZ_220.FZ) ,Calfa_vec1_0,'+','LineWidth',2)
plot(mean(FZ_440.FZ) ,Calfa_vec2_0,'+','LineWidth',2)
plot(mean(FZ_700.FZ) ,Calfa_vec3_0,'+','LineWidth',2)
plot(mean(FZ_900.FZ) ,Calfa_vec4_0,'+','LineWidth',2)
plot(mean(FZ_1120.FZ),Calfa_vec5_0,'+','LineWidth',2)
legend({'Fz$_{220}$','Fz$_{440}$','Fz$_{700}$','Fz$_{900}$','Fz$_{1120}$'})
subplot(2,1,2)
hold on
%plot(TDataSub.KAPPA,FX0_fz_nom_vec,'-')
plot(SA_vec,Calfa_vec1,'-','LineWidth',2)
plot(SA_vec,Calfa_vec2,'-','LineWidth',2)
plot(SA_vec,Calfa_vec3,'-','LineWidth',2)
plot(SA_vec,Calfa_vec4,'-','LineWidth',2)
plot(SA_vec,Calfa_vec5,'-','LineWidth',2)
legend({'Fz$_{220}$','Fz$_{440}$','Fz$_{700}$','Fz$_{900}$','Fz$_{1120}$'})
%% VARIABLE CAMBER LATERAL FY -------------------------------------------------------------> CHECK
% extract data with variable load
TDataGamma = FZ_220;
% Guess values for parameters to be optimised
% [pDy3, pEy3, pEy4, pHy3, pKy3, pVy3, pVy4]
%P0 = [ 5.16349361588200, 0.883205306970767, -4.20062483943437, -0.0313517996563904, 1.34159743861844, -2.92370451981899, -2.81666715709586];
P0 = [ 1, 1, 1, 1, 1, 1, 1 ];
lb = [-1e4, 0, 0, -1e4, -1e4, -1e4, -1e4];
ub = [1e4, 1, 1, 1e4, 1e4, 1e4, 1e4];
KAPPA_vec = TDataGamma.SL;
ALPHA_vec = TDataGamma.SA;
GAMMA_vec = TDataGamma.IA;
FY_vec = TDataGamma.FY;
FZ_vec = TDataGamma.FZ;
SA_vec = min(ALPHA_vec):0.001:max(ALPHA_vec);
zeros_vec = zeros(size(SA_vec));
ones_vec = ones(size(SA_vec));
FZ0 = mean(TDataGamma.FZ);
[P_varGamma,~,~] = fmincon(@(P)resid_pure_Fy_varGamma(P,FY_vec, ALPHA_vec,GAMMA_vec,FZ0, tyre_coeffs),...
P0,[],[],[],[],lb,ub);
% Change tyre data with new optimal values
tyre_coeffs.pDy3 = P_varGamma(1);
tyre_coeffs.pEy3 = P_varGamma(2);
tyre_coeffs.pEy4 = P_varGamma(3);
tyre_coeffs.pHy3 = P_varGamma(4);
tyre_coeffs.pKy3 = P_varGamma(5);
tyre_coeffs.pVy3 = P_varGamma(6);
tyre_coeffs.pVy4 = P_varGamma(7);
FY0_varGamma_vec1 = MF96_FY0_vec(zeros_vec, SA_vec, mean(GAMMA_0.IA).*ones_vec, FZ0*ones_vec,tyre_coeffs);
FY0_varGamma_vec2 = MF96_FY0_vec(zeros_vec, SA_vec, mean(GAMMA_1.IA).*ones_vec, FZ0*ones_vec,tyre_coeffs);
FY0_varGamma_vec3 = MF96_FY0_vec(zeros_vec, SA_vec, mean(GAMMA_2.IA).*ones_vec, FZ0*ones_vec,tyre_coeffs);
FY0_varGamma_vec4 = MF96_FY0_vec(zeros_vec, SA_vec, mean(GAMMA_3.IA).*ones_vec, FZ0*ones_vec,tyre_coeffs);
FY0_varGamma_vec5 = MF96_FY0_vec(zeros_vec, SA_vec, mean(GAMMA_4.IA).*ones_vec, FZ0*ones_vec,tyre_coeffs);
figure('Name','Fy0 vs Gamma')
plot(ALPHA_vec,TDataGamma.FY,'.')
hold on
plot(SA_vec,FY0_varGamma_vec1,'-', LineWidth=1.5)
plot(SA_vec,FY0_varGamma_vec2,'-', LineWidth=1.5)
plot(SA_vec,FY0_varGamma_vec3,'-', LineWidth=1.5)
plot(SA_vec,FY0_varGamma_vec4,'-', LineWidth=1.5)
plot(SA_vec,FY0_varGamma_vec5,'-', LineWidth=1.5)
xlabel('$\alpha$ [rad]')
ylabel('$F_{y0}$ [N]')
legend('','$F_y$ with $\gamma=0$')
% Calculate the residuals with the optimal solution found above
res_Fy0_varGamma = resid_pure_Fy_varGamma(P_varGamma,FY_vec, ALPHA_vec,GAMMA_vec,tyre_coeffs.FZ0, tyre_coeffs);
% R-squared is
% 1-SSE/SST
% SSE/SST = res_Fx0_nom
% SSE is the sum of squared error, SST is the sum of squared total
fprintf('R-squared = %6.3f\n',1-res_Fy0_varGamma);
[alpha__y, By, Cy, Dy, Ey, SVy, ~, ~, ~] = MF96_FY0_coeffs(0, 0, GAMMA_vec(3), tyre_coeffs.FZ0, tyre_coeffs);
%
fprintf('By = %6.3f\n',By);
fprintf('Cy = %6.3f\n',Cy);
fprintf('mu_y = %6.3f\n',Dy/tyre_coeffs.FZ0);
fprintf('Ey = %6.3f\n',Ey);
fprintf('SVy = %6.3f\n',SVy);
fprintf('alpha_y = %6.3f\n',alpha__y);
fprintf('Ky = %6.3f\n',By*Cy*Dy/tyre_coeffs.FZ0);
%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% FX & FY COMB %
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% INITIALISATION ---------------------------------------------------------
clc
clearvars -except tyre_coeffs
%% SELECT TYRE DATA -------------------------------------------------------
%dataset path
data_set_path = 'TTC_dataset/';
% dataset selection and loading
% Hoostier:----------------------------------------------------------------
%data_set = 'Hoosier_B1464run23'; % pure lateral forces
data_set = 'Hoosier_B1464run30'; % braking/traction (pure log. force) + combined
diameter = 18*2.56; % Converting inches to cm
Fz0 = 220; % [N] nominal load is given
R0 = diameter/2/100; % [m] get from nominal load R0 (m)
to_rad = pi/180;
to_deg = 180/pi;
fprintf('Loading dataset ...')
switch data_set
case 'Hoosier_B1464run23'
load ([data_set_path, 'Hoosier_B1464run23.mat']); % pure lateral
cut_start = 27760;
cut_end = 54500;
case 'Hoosier_B1464run30'
load ([data_set_path, 'Hoosier_B1464run30.mat']); % pure longitudinal
cut_start = 19028;
cut_end = 37643;
otherwise
error('Not found dataset: `%s`\n', data_set) ;
end
% select dataset portion
smpl_range = cut_start:cut_end;
fprintf('completed!\n')
%% PLOT RAW DATA ----------------------------------------------------------
figure
tiledlayout(6,1)
ax_list(1) = nexttile; y_range = [min(min(-FZ),0) round(max(-FZ)*1.1)];
plot(-FZ)
hold on
plot([cut_start cut_start],y_range,'--r')
plot([cut_end cut_end],y_range,'--r')
title('Vertical force')
xlabel('Samples [-]')
ylabel('[N]')
ax_list(2) = nexttile; y_range = [min(min(IA),0) round(max(IA)*1.1)];
plot(IA)
hold on
plot([cut_start cut_start],y_range,'--r')
plot([cut_end cut_end],y_range,'--r')
title('Camber angle')
xlabel('Samples [-]')
ylabel('[deg]')
ax_list(3) = nexttile; y_range = [min(min(SA),0) round(max(SA)*1.1)];
plot(SA)
hold on
plot([cut_start cut_start],y_range,'--r')
plot([cut_end cut_end],y_range,'--r')
title('Side slip')
xlabel('Samples [-]')
ylabel('[deg]')
ax_list(4) = nexttile; y_range = [min(min(SL),0) round(max(SL)*1.1)];
plot(SL)
hold on
plot([cut_start cut_start],y_range,'--r')
plot([cut_end cut_end],y_range,'--r')
title('Longitudinal slip')
xlabel('Samples [-]')
ylabel('[-]')
ax_list(5) = nexttile; y_range = [min(min(P),0) round(max(P)*1.1)];
plot(P)
hold on
plot([cut_start cut_start],y_range,'--r')
plot([cut_end cut_end],y_range,'--r')
title('Tyre pressure')
xlabel('Samples [-]')
ylabel('[psi]')
ax_list(6) = nexttile; y_range = [min(min(TSTC),0) round(max(TSTC)*1.1)];
plot(TSTC,'DisplayName','Center')
hold on
plot(TSTI,'DisplayName','Internal')
plot(TSTO,'DisplayName','Outboard')
hold on
plot([cut_start cut_start],y_range,'--r')
plot([cut_end cut_end],y_range,'--r')
title('Tyre temperatures')
xlabel('Samples [-]')
ylabel('[degC]')
linkaxes(ax_list,'x')
%figure()
%plot(SA,FY)
%% SELECT SPECIFIC DATA ---------------------------------------------------
% Cut crappy data and select only 80 psi data
vec_samples = 1:1:length(smpl_range);
tyre_data = table(); % create empty table
% store raw data in table
tyre_data.SL = SL(smpl_range); % Longitudinal slip
tyre_data.SA = SA(smpl_range)*to_rad; % Side slip
tyre_data.FZ = -FZ(smpl_range); % 0.453592 lb/kg % Vertical force
tyre_data.FX = FX(smpl_range); % Longitudinal force
tyre_data.FY = -FY(smpl_range); % Lateral force
tyre_data.MZ = MZ(smpl_range); % Self aligning moment
tyre_data.IA = IA(smpl_range)*to_rad; % Camber angle
% Extract points at constant camber inclination angle
GAMMA_tol = 0.05*to_rad;
idx.GAMMA_0 = 0.0*to_rad-GAMMA_tol < tyre_data.IA & tyre_data.IA < 0.0*to_rad+GAMMA_tol;
idx.GAMMA_1 = 1.0*to_rad-GAMMA_tol < tyre_data.IA & tyre_data.IA < 1.0*to_rad+GAMMA_tol;
idx.GAMMA_2 = 2.0*to_rad-GAMMA_tol < tyre_data.IA & tyre_data.IA < 2.0*to_rad+GAMMA_tol;
idx.GAMMA_3 = 3.0*to_rad-GAMMA_tol < tyre_data.IA & tyre_data.IA < 3.0*to_rad+GAMMA_tol;
idx.GAMMA_4 = 4.0*to_rad-GAMMA_tol < tyre_data.IA & tyre_data.IA < 4.0*to_rad+GAMMA_tol;
idx.GAMMA_5 = 5.0*to_rad-GAMMA_tol < tyre_data.IA & tyre_data.IA < 5.0*to_rad+GAMMA_tol;
GAMMA_0 = tyre_data( idx.GAMMA_0, : );
GAMMA_1 = tyre_data( idx.GAMMA_1, : );
GAMMA_2 = tyre_data( idx.GAMMA_2, : );
GAMMA_3 = tyre_data( idx.GAMMA_3, : );
GAMMA_4 = tyre_data( idx.GAMMA_4, : );
GAMMA_5 = tyre_data( idx.GAMMA_5, : );
% Extract points at constant vertical load
% 200, 150, 50, 250, 100
FZ_tol = 100;
idx.FZ_220 = 220-FZ_tol < tyre_data.FZ & tyre_data.FZ < 220+FZ_tol;
idx.FZ_440 = 440-FZ_tol < tyre_data.FZ & tyre_data.FZ < 440+FZ_tol;
idx.FZ_700 = 700-FZ_tol < tyre_data.FZ & tyre_data.FZ < 700+FZ_tol;
idx.FZ_900 = 900-FZ_tol < tyre_data.FZ & tyre_data.FZ < 900+FZ_tol;
idx.FZ_1120 = 1120-FZ_tol < tyre_data.FZ & tyre_data.FZ < 1120+FZ_tol;
FZ_220 = tyre_data( idx.FZ_220, : );
FZ_440 = tyre_data( idx.FZ_440, : );
FZ_700 = tyre_data( idx.FZ_700, : );
FZ_900 = tyre_data( idx.FZ_900, : );
FZ_1120 = tyre_data( idx.FZ_1120, : );
% The slip angle is varied continuously between -4 and +12° and then
% between -12° and +4° for the pure slip case
% The slip angle is varied step wise for longitudinal slip tests
% 0° , - 3° , -6 °
SA_tol = 0.5*to_rad;
idx.SA_0 = 0-SA_tol < tyre_data.SA & tyre_data.SA < 0+SA_tol;
idx.SA_3neg = -(3*to_rad+SA_tol) < tyre_data.SA & tyre_data.SA < -3*to_rad+SA_tol;
idx.SA_6neg = -(6*to_rad+SA_tol) < tyre_data.SA & tyre_data.SA < -6*to_rad+SA_tol;
SA_0 = tyre_data( idx.SA_0, : );
SA_3neg = tyre_data( idx.SA_3neg, : );
SA_6neg = tyre_data( idx.SA_6neg, : );
figure()
tiledlayout(3,1)
ax_list(1) = nexttile;
plot(tyre_data.IA*to_deg)
hold on
plot(vec_samples(idx.GAMMA_0),GAMMA_0.IA*to_deg,'.');
plot(vec_samples(idx.GAMMA_1),GAMMA_1.IA*to_deg,'.');
plot(vec_samples(idx.GAMMA_2),GAMMA_2.IA*to_deg,'.');
plot(vec_samples(idx.GAMMA_3),GAMMA_3.IA*to_deg,'.');
plot(vec_samples(idx.GAMMA_4),GAMMA_4.IA*to_deg,'.');
plot(vec_samples(idx.GAMMA_5),GAMMA_5.IA*to_deg,'.');
title('Camber angle')
xlabel('Samples [-]')
ylabel('[deg]')
ax_list(2) = nexttile;
plot(tyre_data.FZ)
hold on
plot(vec_samples(idx.FZ_220),FZ_220.FZ,'.');
plot(vec_samples(idx.FZ_440),FZ_440.FZ,'.');
plot(vec_samples(idx.FZ_700),FZ_700.FZ,'.');
plot(vec_samples(idx.FZ_900),FZ_900.FZ,'.');
plot(vec_samples(idx.FZ_1120),FZ_1120.FZ,'.');
title('Vertical force')
xlabel('Samples [-]')
ylabel('[N]')
ax_list(3) = nexttile;
plot(tyre_data.SA*to_deg)
hold on
plot(vec_samples(idx.SA_0), SA_0.SA*to_deg,'.');
plot(vec_samples(idx.SA_3neg),SA_3neg.SA*to_deg,'.');
plot(vec_samples(idx.SA_6neg),SA_6neg.SA*to_deg,'.');
title('Slide slip')
xlabel('Samples [-]')
ylabel('[rad]')
%% PLOT SELECTED DATA -----------------------------------------------------
[TData0, ~] = intersect_table_data( SA_0, GAMMA_0, FZ_220 );
figure('Name','Selected-data')
plot_selected_data(TData0);
%% PURE LONGITUDINAL SLIP FX, Fz=Fz_nom= 220N and camber=0 alpha = 0 VX= 10 --------------> DONE
[TData0, ~] = intersect_table_data( SA_0, GAMMA_0, FZ_220 );
% Fit the coeffs {pCx1, pDx1, pEx1, pEx4, pKx1, pHx1, pVx1}
FZ0 = mean(TData0.FZ);
zeros_vec = zeros(size(TData0.SL));
ones_vec = ones(size(TData0.SL));
FX0_guess = MF96_FX0_vec(TData0.SL,zeros_vec , zeros_vec, tyre_coeffs.FZ0*ones_vec, tyre_coeffs);
% check guess
%figure()
%plot(TData0.SL,TData0.FX,'.')
%hold on
%plot(TData0.SL,FX0_guess,'-')
% Plot raw data and initial guess
% figure()
% plot(TDataSub.KAPPA,TDataSub.FX,'o')
% hold on
% plot(TDataSub.KAPPA,FX0_guess,'x')
% Guess values for parameters to be optimised
% [pCx1 pDx1 pEx1 pEx4 pHx1 pKx1 pVx1]
P0 = [ 1, 2, 1, 0, 0, 1, 0];
% NOTE: many local minima => limits on parameters are fundamentals
% Limits for parameters to be optimised
% 1< pCx1 < 2
% 0< pEx1 < 1
% [pCx1 pDx1 pEx1 pEx4 pHx1 pKx1 pVx1]
lb = [1, 0.1, 0, 0, -10, 0, -10];
ub = [2, 4, 1, 1, 10, 100, 10];
KAPPA_vec = TData0.SL;
FX_vec = TData0.FX;
% LSM_pure_Fx returns the residual, so minimize the residual varying X. It
% is an unconstrained minimization problem
[P_fz_nom,fval,exitflag] = fmincon(@(P)resid_pure_Fx(P,FX_vec, KAPPA_vec,0,FZ0, tyre_coeffs),...
P0,[],[],[],[],lb,ub);
% Update tyre data with new optimal values
tyre_coeffs.pCx1 = P_fz_nom(1) ; % 1
tyre_coeffs.pDx1 = P_fz_nom(2) ;
tyre_coeffs.pEx1 = P_fz_nom(3) ;
tyre_coeffs.pEx4 = P_fz_nom(4) ;
tyre_coeffs.pHx1 = P_fz_nom(5) ;
tyre_coeffs.pKx1 = P_fz_nom(6) ;
tyre_coeffs.pVx1 = P_fz_nom(7) ;
SL_vec = -0.3:0.001:0.3;
FX0_fz_nom_vec = MF96_FX0_vec(SL_vec,zeros(size(SL_vec)) , zeros(size(SL_vec)), ...
FZ0.*ones(size(SL_vec)),tyre_coeffs);
figure()
plot(TData0.SL,TData0.FX,'.')
hold on
plot(SL_vec,FX0_fz_nom_vec,'-','LineWidth',2)
xlabel('$\kappa$ [-]')
ylabel('$F_{x0}$ [N]')
legend('Raw data','Fitting',Location='best')
title('Fit pure longitudinal force $F_{x0}$ with $F_z=F_{znom}= 220$N, $\gamma=0$ , $\alpha=0$')
%% VARIABLE LOAD LONGITUDINAL FX ----------------------------------------------------------> DONE
% extract data with variable load
[TDataDFz, ~] = intersect_table_data( SA_0, GAMMA_0 );
KAPPA_vec = TDataDFz.SL;
FX_vec = TDataDFz.FX;
FZ_vec = TDataDFz.FZ;
zeros_vec = zeros(size(TDataDFz.SL));
ones_vec = ones(size(TDataDFz.SL));
FX0_guess = MF96_FX0_vec(KAPPA_vec,zeros_vec , zeros_vec, FZ_vec, tyre_coeffs);
SL_vec = min(KAPPA_vec):1e-4:max(KAPPA_vec);
tmp_zeros = zeros(size(SL_vec));
tmp_ones = ones(size(SL_vec));
% Guess values for parameters to be optimised
% [pDx2 pEx2 pEx3 pHx2 pKx2 pKx3 pVx2]
P0 = [ 0, 0, 0, 0, 0, 0, 0];
lb = [];
ub = [];
% LSM_pure_Fx returns the residual, so minimize the residual varying X. It
% is an unconstrained minimization problem
[P_dfz,~,~] = fmincon(@(P)resid_pure_Fx_varFz(P,FX_vec, KAPPA_vec,0,FZ_vec, tyre_coeffs),...
P0,[],[],[],[],lb,ub);
disp(exitflag)
% Change tyre data with new optimal values
tyre_coeffs.pDx2 = P_dfz(1) ; % 1
tyre_coeffs.pEx2 = P_dfz(2) ;
tyre_coeffs.pEx3 = P_dfz(3) ;
tyre_coeffs.pHx2 = P_dfz(4) ;
tyre_coeffs.pKx2 = P_dfz(5) ;
tyre_coeffs.pKx3 = P_dfz(6) ;
tyre_coeffs.pVx2 = P_dfz(7) ;
res_FX0_dfz_vec = resid_pure_Fx_varFz(P_dfz,FX_vec,KAPPA_vec,0 , FZ_vec,tyre_coeffs);
% Visulisation--- use mean(Fz to avoid oscilltion)
FX0_fz_var_vec1 = MF96_FX0_vec(SL_vec,tmp_zeros ,tmp_zeros, mean(FZ_220.FZ)*tmp_ones,tyre_coeffs);
FX0_fz_var_vec2 = MF96_FX0_vec(SL_vec,tmp_zeros ,tmp_zeros, mean(FZ_700.FZ)*tmp_ones,tyre_coeffs);
FX0_fz_var_vec3 = MF96_FX0_vec(SL_vec,tmp_zeros ,tmp_zeros, mean(FZ_900.FZ)*tmp_ones,tyre_coeffs);
FX0_fz_var_vec4 = MF96_FX0_vec(SL_vec,tmp_zeros ,tmp_zeros, mean(FZ_1120.FZ)*tmp_ones,tyre_coeffs);
figure('Name','Fx0(Fz0)')
plot(TDataDFz.SL,TDataDFz.FX,'.')
hold on
%plot(TDataSub.KAPPA,FX0_fz_nom_vec,'-')
%plot(SL_vec,FX0_dfz_vec,'-','LineWidth',2)
plot(SL_vec,FX0_fz_var_vec1,'-','LineWidth',2)
plot(SL_vec,FX0_fz_var_vec2,'-','LineWidth',2)
plot(SL_vec,FX0_fz_var_vec3,'-','LineWidth',2)
plot(SL_vec,FX0_fz_var_vec4,'-','LineWidth',2)
xlabel('$\kappa$ [-]')
ylabel('$F_{x0}$ [N]')
%% CORNERING STIFFNESS
[kappa__x, Bx, Cx, Dx, Ex, SVx] =MF96_FX0_coeffs(0, 0, 0, mean(FZ_220.FZ), tyre_coeffs);
Calfa_vec1_0 = magic_formula_stiffness(kappa__x, Bx, Cx, Dx, Ex, SVx);
[kappa__x, Bx, Cx, Dx, Ex, SVx] =MF96_FX0_coeffs(0, 0, 0, mean(FZ_700.FZ), tyre_coeffs);
Calfa_vec2_0 = magic_formula_stiffness(kappa__x, Bx, Cx, Dx, Ex, SVx);
[kappa__x, Bx, Cx, Dx, Ex, SVx] =MF96_FX0_coeffs(0, 0, 0, mean(FZ_900.FZ), tyre_coeffs);
Calfa_vec3_0 = magic_formula_stiffness(kappa__x, Bx, Cx, Dx, Ex, SVx);
[kappa__x, Bx, Cx, Dx, Ex, SVx] =MF96_FX0_coeffs(0, 0, 0, mean(FZ_1120.FZ), tyre_coeffs);
Calfa_vec4_0 = magic_formula_stiffness(kappa__x, Bx, Cx, Dx, Ex, SVx);
Calfa_vec1 = MF96_CorneringStiffness(SL_vec,tmp_zeros ,tmp_zeros, mean(FZ_220.FZ)*tmp_ones,tyre_coeffs);
Calfa_vec2 = MF96_CorneringStiffness(SL_vec,tmp_zeros ,tmp_zeros, mean(FZ_700.FZ)*tmp_ones,tyre_coeffs);
Calfa_vec3 = MF96_CorneringStiffness(SL_vec,tmp_zeros ,tmp_zeros, mean(FZ_900.FZ)*tmp_ones,tyre_coeffs);
Calfa_vec4 = MF96_CorneringStiffness(SL_vec,tmp_zeros ,tmp_zeros, mean(FZ_1120.FZ)*tmp_ones,tyre_coeffs);
figure('Name','C_alpha')
subplot(2,1,1)
hold on
%plot(TDataSub.KAPPA,FX0_fz_nom_vec,'-')
plot(mean(FZ_220.FZ),Calfa_vec1_0,'+','LineWidth',2)
plot(mean(FZ_700.FZ),Calfa_vec3_0,'+','LineWidth',2)
plot(mean(FZ_900.FZ),Calfa_vec4_0,'+','LineWidth',2)
plot(mean(FZ_1120.FZ),Calfa_vec2_0,'+','LineWidth',2)
legend({'Fz_{220}','Fz_{700}','Fz_{900}','Fz_{1120}'})
subplot(2,1,2)
hold on
%plot(TDataSub.KAPPA,FX0_fz_nom_vec,'-')
plot(SL_vec,Calfa_vec1,'-','LineWidth',2)
plot(SL_vec,Calfa_vec2,'-','LineWidth',2)
plot(SL_vec,Calfa_vec3,'-','LineWidth',2)
plot(SL_vec,Calfa_vec4,'-','LineWidth',2)
legend({'Fz_{220}','Fz_{700}','Fz_{900}','Fz_{1120}'})
%% VARIABLE CAMBER LONGITUDINAL -----------------------------------------------------------> DONE
% extract data with variable load
[TDataGamma, ~] = intersect_table_data( SA_0, FZ_220 );
% Fit the coeffs { pDx3}
% Guess values for parameters to be optimised
P0 = [0];
% NOTE: many local minima => limits on parameters are fundamentals
% Limits for parameters to be optimised
% 1< pCx1 < 2
% 0< pEx1 < 1
%lb = [0, 0, 0, 0, 0, 0, 0];
%ub = [2, 1e6,1, 1,1e1,1e2,1e2];
lb = [];
ub = [];
zeros_vec = zeros(size(TDataGamma.SL));
ones_vec = ones(size(TDataGamma.SL));
KAPPA_vec = TDataGamma.SL;
GAMMA_vec = TDataGamma.IA;
FX_vec = TDataGamma.FX;
FZ_vec = TDataGamma.FZ;
figure()
plot(KAPPA_vec,FX_vec);
% LSM_pure_Fx returns the residual, so minimize the residual varying X. It
% is an unconstrained minimization problem
[P_varGamma,~,~] = fmincon(@(P)resid_pure_Fx_varGamma(P,FX_vec, KAPPA_vec,GAMMA_vec,tyre_coeffs.FZ0, tyre_coeffs),...
P0,[],[],[],[],lb,ub);
% Change tyre data with new optimal values
tyre_coeffs.pDx3 = P_varGamma(1) ; % 1
FX0_varGamma_vec0 = MF96_FX0_vec(KAPPA_vec,zeros_vec , GAMMA_0.IA, tyre_coeffs.FZ0*ones_vec,tyre_coeffs);
FX0_varGamma_vec2 = MF96_FX0_vec(KAPPA_vec, zeros_vec , GAMMA_2.IA, tyre_coeffs.FZ0*ones_vec,tyre_coeffs);
FX0_varGamma_vec4 = MF96_FX0_vec(KAPPA_vec, zeros_vec , GAMMA_4.IA, tyre_coeffs.FZ0*ones_vec,tyre_coeffs);
figure('Name','Fx0(Gamma)')
plot(KAPPA_vec,TDataGamma.FX,'.', 'DisplayName','Raw')
hold on
plot(KAPPA_vec,FX0_varGamma_vec0,'-', 'LineWidth',1.5, 'DisplayName', 'Fit $\gamma = 0$')
plot(KAPPA_vec,FX0_varGamma_vec2,'-', 'LineWidth',1.5, 'DisplayName', 'Fit $\gamma = 2$')
plot(KAPPA_vec,FX0_varGamma_vec4,'-', 'LineWidth',1.5, 'DisplayName', 'Fit $\gamma = 4$')
title('Pure Longitudinal slip at verticle load $F_{z}$ = 220[N], $\alpha = 0$ ')
xlabel('$\kappa$ [-]')
ylabel('$F_{x}$ [N]')
legend('Location','best')
% Calculate the residuals with the optimal solution found above
res_Fx0_varGamma = resid_pure_Fx_varGamma(P_varGamma,FX_vec, KAPPA_vec,GAMMA_vec,tyre_coeffs.FZ0, tyre_coeffs);
% R-squared is
% 1-SSE/SST
% SSE/SST = res_Fx0_nom
% SSE is the sum of squared error, SST is the sum of squared total
fprintf('R-squared = %6.3f\n',1-res_Fx0_varGamma);
[kappa__x, Bx, Cx, Dx, Ex, SVx] = MF96_FX0_coeffs(0, 0, GAMMA_vec(3), tyre_coeffs.FZ0, tyre_coeffs);
%
fprintf('Bx = %6.3f\n',Bx);
fprintf('Cx = %6.3f\n',Cx);
fprintf('mux = %6.3f\n',Dx/tyre_coeffs.FZ0);
fprintf('Ex = %6.3f\n',Ex);
fprintf('SVx = %6.3f\n',SVx);
fprintf('kappa_x = %6.3f\n',kappa__x);
fprintf('Kx = %6.3f\n',Bx*Cx*Dx/tyre_coeffs.FZ0);
%% COMBINED LONGITUDINAL FX ----------------------------------------------------------------> DONE
[TDataComb, ~] = intersect_table_data(GAMMA_0, FZ_220);
% Initialise:--------------------------------------------------------------
FZ0 = mean(TDataComb.FZ);
zeros_vec = zeros(size(TDataComb.SL));
ones_vec = ones(size(TDataComb.SL));
ALPHA_comb_vec = TDataComb.SA;
FX_comb_vec = TDataComb.FX;
KAPPA_comb_vec = TDataComb.SL;
% Optimisation:------------------------------------------------------------
% Guess for parameters to be optimised:
% [rBx1, rBx2, rCx1, rHx1]
P0 = [ 10, 5, 1, 0];
lb = 1;
ub = 10;
% Pure parameters optimisation:
FX0_vec = MF96_FX0_vec(KAPPA_comb_vec, zeros_vec, zeros_vec, FZ0.*ones_vec, tyre_coeffs);
[P_comb,~,~] = fmincon(@(P)resid_comb_Fx(P,FX_comb_vec, KAPPA_comb_vec,ALPHA_comb_vec,0,FZ0,tyre_coeffs,FX0_vec),...
P0,[],[],[],[],lb,ub);
% Update tyre data with new optimal values
tyre_coeffs.rBx1 = P_comb(1) ;
tyre_coeffs.rBx2 = P_comb(2) ;
tyre_coeffs.rCx1 = P_comb(3) ;
tyre_coeffs.rHx1 = P_comb(4) ;
fx_SA0 = MF96_FX_vec(FX0_vec, KAPPA_comb_vec, mean(SA_0.SA).*ones_vec , zeros_vec, FZ0.*ones_vec, tyre_coeffs);
fx_SA3 = MF96_FX_vec(FX0_vec, KAPPA_comb_vec, mean(SA_3neg.SA).*ones_vec, zeros_vec, FZ0.*ones_vec, tyre_coeffs);
fx_SA6 = MF96_FX_vec(FX0_vec, KAPPA_comb_vec, mean(SA_6neg.SA).*ones_vec, zeros_vec, FZ0.*ones_vec, tyre_coeffs);
figure, grid on, hold on;
plot(KAPPA_comb_vec*to_deg,TDataComb.FX,'.')
plot(KAPPA_comb_vec*to_deg,fx_SA0,'LineWidth',2,Color = [0.9290 0.6940 0.1250])
plot(KAPPA_comb_vec*to_deg,fx_SA3,'LineWidth',2,Color = [0.4940 0.1840 0.5560])
plot(KAPPA_comb_vec*to_deg,fx_SA6,'LineWidth',2,Color = [0.4660 0.6740 0.1880])
xlabel('$k(-)$')
ylabel('$F_x[N]$')
ylim('padded')
legend('Raw Data','Fit $\alpha$=0 deg',...
'Fit $\alpha$=-3 deg','Fit $\alpha$=-6 deg',Location='southeast')
title('Combined Slip Longitudinal Force')
%% PLOT Gx --------------------------------------------------------------------------------> CHECK
sa = [0,3,6,10,20]; % side slip in radians
sl = linspace(-1,1,1e4); % longitudinal slip
Gxa_k = zeros(length(sa),length(sl));
for i = 1:length(sa)
for j = 1:length(sl)
[Gxa_k(i,j),~,~] = MF96_FXFYCOMB_coeffs(sl(j), sa(i)*to_rad, 0, FZ0, tyre_coeffs); %alpha row, k column
end
end
figure, grid on, hold on;
plot(sl,Gxa_k , LineWidth=1.5)
xlabel('longitudinal slip $k$(-)')
ylabel('$G_{xa}(-)$')
ylim('padded')
leg = cell(size(sa));
for i = 1:length(sa)
leg{i} = ['$\alpha$ = ',num2str(sa(i)),' deg'];
end
legend(leg,Location="best")
title('Weighting function $G_{xa}$ as a function of $k$')
hold off
sa = linspace(-20,20,1e4);
sl = [0,0.1,0.2,0.5,0.8,1];
Gxa_a = zeros(length(sl),length(sa));
for i = 1:length(sl)
for j = 1:length(sa)
Gxa_a(i,j) = MF96_FXFYCOMB_coeffs(sl(i), sa(j), 0, FZ0, tyre_coeffs); % k row, alpha column
end
end
figure, grid on, hold on;
for i = 1:length(sl)
plot(sa,Gxa_a(i,:), LineWidth=1.5)
end
xlabel('side slip angle $\alpha$(deg)')
ylabel('$G_{xa}(-)$')
ylim('padded')